Slope Stability Calculator – Preliminary Earth Slope

Introduction

The EstiMate Civil Slope Stability Calculator evaluates the Factor of Safety (FS) for simplified infinite slope models under dry or saturated soil parameters.

Governing Formulas

The Factor of Safety against slope failure is defined as the ratio of shear strength ($ \tau_f $) to active shear stress ($ \tau_d $) along the slip surface:

Infinite Dry Slope with Cohesionless Soil ($ c = 0 $):
$ FS = \frac{\tan\phi}{\tan\beta} $ (where $ \phi $ is the internal friction angle, and $ \beta $ is the slope angle).
Infinite Slope with Cohesion and Seepage:
$ FS = \frac{c' + (\gamma_{sat} - \gamma_w) H \cos^2\beta \tan\phi'}{\gamma_{sat} H \sin\beta \cos\beta} $
Where $ H $ is depth of the failure plane, and $ \gamma_w $ is the unit weight of water ($ 9.81\text{ kN/m}^3 $).

Key Assumptions

Infinite slope model analysis relies on these critical assumptions:

The slip surface runs parallel to the ground surface.
The slope is assumed to be of infinite lateral extent, neglecting boundary effects at the top and toe of the slope.
Soil shear strength conforms strictly to the Mohr-Coulomb failure criterion: $ s = c' + \sigma' \tan\phi' $.

Practical Example Calculation

Consider a dry infinite slope composed of sandy soil with a friction angle $ \phi = 30^\circ $. The slope angle is measured at $ \beta = 22^\circ $:

Factor of Safety ($FS$):
$ FS = \frac{\tan 30^\circ}{\tan 22^\circ} = \frac{0.5773}{0.4040} \approx 1.43 $
Evaluation: Since $ FS = 1.43 > 1.0 $ (and typically $ \ge 1.3 $), the slope is considered stable under dry, static conditions.

Practical Limitations

The infinite slope model is not applicable for:

Complex, multi-layered soil stratigraphy or slopes with varying geometry.
Evaluating circular slip failures common in deep clay cuts (where Bishop's or Fellenius' method of slices is required).
Seismic slope stability (unless pseudo-static horizontal acceleration coefficient $ k_h $ is factored into the normal and tangential force analysis).

Standard References

For slope stability theory and design limits, see:

Das, B. M. Principles of Geotechnical Engineering.
Fellenius, W. Calculation of the Stability of Earth Dams (Method of Slices theory).